An error estimate in the EFG method. (English) Zbl 0910.73060

Summary: We propose local and global error estimates for the element-free Galerkin (EFG) method. The essence of proposed error estimates is to use the difference between the values of the projected stress and the values of stress given directly by the EFG solution. The stress projection can be obtained by taking product of shape function based on a domain of influence with the stresses at nodes. We find that the effectivity index can be optimized if the domain of influence in the stress projection procedure is the smallest one that retains regularity of the matrices in EFG. Numerical one- and two-dimensional examples illustrate the good effectiveness of the proposed error estimator in the global energy norm and in the local error estimates.


74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N15 Error bounds for boundary value problems involving PDEs
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